When did this invasion start? What was the first "shot fired' and what show was it on?

Beginning of '86. The UWF guys were re-introduced at the beginning of January and the first big NJ vs. UWF matches were in early February as I recall.

 

Edit: There wasn't a "shot fired" in the sense of Choshu turning on Fujinami in '82. They actually started the UWF guys working against each other.

The UWF guys did challenge Inoki and the NJPW wrestlers when they first showed up on 12/6/85.

Huh, don't think I ever saw that for whatever reason.

It's on The History of New Japan vs. UWF Vol. 1.